Let ${\mathcal{P}}_r$ denote an almost–prime with at most $r$ prime factors, counted according to multiplicity. In this paper, it is proved that for every sufficiently large even integer $N$, the following equation

$$N=p_1^2+p_2^2+x^3+p_3^3+p_4^3+p_5^3$$

is solvable with $x$ being an almost–prime ${\mathcal{P}}_7$ and the other variables primes. This result constitutes a deepening upon that of previous results.